One side effect of faster training is the increased marginalization of lower potential levels, since those would cap that much faster than currently. And of course, given the current prevailing opinion of the draft as being only measurable in terms of the number of 18 year olds with MVP+ potential as is, this would be even more extreme.
Another side effect would be the increase in the escalation of young player salary compared to current. Of course, that wouldn't be a concern if we were certain that players would never train players who become unaffordable to them, but that's currently not the case.
+2!!
One thought would be an occasional lower potential level guy who actually has higher caps, sort of a diamond in the rough. Maybe they wouldn't be so easily discarded.
Escalation of young player salary would be even more problematical than it already is, as you observe, but just imagine the escalation of transfer prices of higher level potential youths! Out of sight!
I'm not sure introducing more randomness into the potential is the answer, though, since the randomness of the draft is already (to put it charitably) unpopular. I think instead something that made lower potential players more valuable overall would be an appropriate direction to complement this - so, just for a hypothetical, on the general theme of "increase training speed" one might suggest the following implementation:
1. Training speed is increased for skills at lower levels (e.g., training IS for a player with IS 5 will be significantly faster than a player with IS 15).
2. Something similar to the elastic effect, whereby if a player's skill is among his lowest skills, it trains faster, and if it's among his highest, it trains slower.
3. A change to potential caps and salary formulas so that all skills below a certain value (7 or 8) do not affect the player's potential cap and do not significantly boost salary.
4. Some rebalancing of salary and cap calculations and training speed of certain regimes versus others (which would deserve much more analysis than this post is attempting).
So in an environment where those four changes were made, pretty much any player could be trained to be 7 or 8 in every skill plus some additional boosts in their primary skills, so someone wanting to build a homegrown team could still create attractive players even with lower potential players than today, and the utility of the middle potential players could be expanded. There would be incentive to train players with more balance than is usual, with much faster returns and lower salary impact from doing so, which could also shield some of the salary escalation issues.
Of course, the downside here is that at that point, it's essentially a mandate that all players should have 7 in all their secondary skills, which takes some of the variety out of the game. So there'd have to be something to temper that push somewhat. And that's of course the point - changes have ripples and it's important that those effects are understood and accounted for when rebalancing or we get the situation like we're in now, where the changes made to combat the overpowering of outside offense in the early seasons of the game have pretty much rendered inside offenses as the dominant paradigm.